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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "ax = plt.gca()\n",
    "\n",
    "plt.plot([1,1],[0,1],color='red',linewidth=2)\n",
    "plt.plot([1,2],[2,2],color='red',linewidth=2)\n",
    "plt.plot([2,2],[2,1],color='red',linewidth=2)\n",
    "plt.plot([2,3],[1,1],color='red',linewidth=2)\n",
    "\n",
    "plt.text(0.5,2.5,\"S0\",size=14,ha='center')\n",
    "plt.text(1.5,2.5,\"S1\",size=14,ha='center')\n",
    "plt.text(2.5,2.5,\"S2\",size=14,ha='center')\n",
    "plt.text(0.5,1.5,\"S3\",size=14,ha='center')\n",
    "plt.text(1.5,1.5,\"S4\",size=14,ha='center')\n",
    "plt.text(2.5,1.5,\"S5\",size=14,ha='center')\n",
    "plt.text(0.5,0.5,\"S6\",size=14,ha='center')\n",
    "plt.text(1.5,0.5,\"S7\",size=14,ha='center')\n",
    "plt.text(2.5,0.5,\"S8\",size=14,ha='center')\n",
    "\n",
    "plt.text(0.5,2.3,\"start\",ha='center')\n",
    "plt.text(2.5,0.3,\"goal\",ha='center')\n",
    "ax.set_xlim(0,3)\n",
    "ax.set_ylim(0,3)\n",
    "\n",
    "plt.tick_params(axis='both',which='both',bottom='off',top='off',labelbottom='off',right='off',\n",
    "left='off',labelleft='off')\n",
    "line, = plt.plot([0.5],[2.5],marker='o',color='g',markersize='60')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 列表示 ↑，→，↓，←的方向\n",
    "theta_0 = np.array([[np.nan,1,1,np.nan],#S0\n",
    "                    [np.nan,1,np.nan,1],#S1\n",
    "                    [np.nan,np.nan,1,1],#S2\n",
    "                    [1,1,1,np.nan],#S3\n",
    "                    [np.nan,np.nan,1,1],#S4\n",
    "                    [1,np.nan,np.nan,np.nan],#S5\n",
    "                    [1,np.nan,np.nan,np.nan],#S6\n",
    "                    [1,1,np.nan,np.nan],#S7\n",
    "                    ]) #s8为目标，没有策略"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.    0.5   0.5   0.   ]\n [0.    0.5   0.    0.5  ]\n [0.    0.    0.5   0.5  ]\n [0.333 0.333 0.333 0.   ]\n [0.    0.    0.5   0.5  ]\n [1.    0.    0.    0.   ]\n [1.    0.    0.    0.   ]\n [0.5   0.5   0.    0.   ]]\n[0, 1, 0, 3, 0, 1, 0, 3, 0, 3, 0, 3, 6, 3, 6, 3, 6, 3, 0, 3, 6, 3, 4, 7, 4, 7, 4, 3, 4, 7, 8]\n需要的步数：30\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# 将对应于前进方向的θ值转换为百分比以作为概率\n",
    "def simple_convert_into_pi_from_theta(theta):\n",
    "    m,n = theta.shape\n",
    "    pi = np.zeros((m,n))\n",
    "    for i in range(0,m):\n",
    "        pi[i,:] = theta[i,:]/np.nansum(theta[i,:])\n",
    "    pi = np.nan_to_num(pi)\n",
    "    print(pi)\n",
    "    return pi\n",
    "# 根据上一步的移动获取下一步的状态\n",
    "def get_next_s(pi, s):\n",
    "    direction = [\"up\",\"right\",\"down\",\"left\"]\n",
    "    # 根据概率pi[s,:]选择下一步行动\n",
    "    next_direction = np.random.choice(direction, p=pi[s, : ])\n",
    "    if next_direction == \"up\":\n",
    "        s_next = s - 3\n",
    "    if next_direction == \"right\":\n",
    "        s_next = s + 1\n",
    "    if next_direction == \"down\":\n",
    "        s_next = s + 3\n",
    "    if next_direction == \"left\":\n",
    "        s_next = s - 1\n",
    "    return s_next\n",
    "    \n",
    "def goal_maze(pi):\n",
    "    s = 0\n",
    "    state_history = [0] #记录移动轨迹\n",
    "    while(1):\n",
    "        next_s = get_next_s(pi,s)\n",
    "        state_history.append(next_s)\n",
    "        if next_s == 8:\n",
    "            break\n",
    "        else:\n",
    "            s = next_s\n",
    "    return state_history\n",
    "# 初始策略\n",
    "pi_0 = simple_convert_into_pi_from_theta(theta_0)\n",
    "state_history = goal_maze(pi_0)\n",
    "print(state_history)\n",
    "print(f\"需要的步数：{len(state_history)-1}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.         0.5        0.5        0.        ]\n [0.         0.5        0.         0.5       ]\n [0.         0.         0.5        0.5       ]\n [0.33333333 0.33333333 0.33333333 0.        ]\n [0.         0.         0.5        0.5       ]\n [1.         0.         0.         0.        ]\n [1.         0.         0.         0.        ]\n [0.5        0.5        0.         0.        ]]\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ],
      "text/html": "\n<link rel=\"stylesheet\"\nhref=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\ncss/font-awesome.min.css\">\n<script language=\"javascript\">\n  function isInternetExplorer() {\n    ua = navigator.userAgent;\n    /* MSIE used to detect old browsers and Trident used to newer ones*/\n    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n  }\n\n  /* Define the Animation class */\n  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n    this.img_id = img_id;\n    this.slider_id = slider_id;\n    this.loop_select_id = loop_select_id;\n    this.interval = interval;\n    this.current_frame = 0;\n    this.direction = 0;\n    this.timer = null;\n    this.frames = new Array(frames.length);\n\n    for (var i=0; i<frames.length; i++)\n    {\n     this.frames[i] = new Image();\n     this.frames[i].src = frames[i];\n    }\n    var slider = document.getElementById(this.slider_id);\n    slider.max = this.frames.length - 1;\n    if (isInternetExplorer()) {\n        // switch from oninput to onchange because IE <= 11 does not conform\n        // with W3C specification. It ignores oninput and onchange behaves\n        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n        slider.setAttribute('oninput', null);\n    }\n    this.set_frame(this.current_frame);\n  }\n\n  Animation.prototype.get_loop_state = function(){\n    var button_group = document[this.loop_select_id].state;\n    for (var i = 0; i < button_group.length; i++) {\n        var button = button_group[i];\n        if (button.checked) {\n            return button.value;\n        }\n    }\n    return undefined;\n  }\n\n  Animation.prototype.set_frame = function(frame){\n    this.current_frame = frame;\n    document.getElementById(this.img_id).src =\n            this.frames[this.current_frame].src;\n    document.getElementById(this.slider_id).value = this.current_frame;\n  }\n\n  Animation.prototype.next_frame = function()\n  {\n    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n  }\n\n  Animation.prototype.previous_frame = function()\n  {\n    this.set_frame(Math.max(0, this.current_frame - 1));\n  }\n\n  Animation.prototype.first_frame = function()\n  {\n    this.set_frame(0);\n  }\n\n  Animation.prototype.last_frame = function()\n  {\n    this.set_frame(this.frames.length - 1);\n  }\n\n  Animation.prototype.slower = function()\n  {\n    this.interval /= 0.7;\n    if(this.direction > 0){this.play_animation();}\n    else if(this.direction < 0){this.reverse_animation();}\n  }\n\n  Animation.prototype.faster = function()\n  {\n    this.interval *= 0.7;\n    if(this.direction > 0){this.play_animation();}\n    else if(this.direction < 0){this.reverse_animation();}\n  }\n\n  Animation.prototype.anim_step_forward = function()\n  {\n    this.current_frame += 1;\n    if(this.current_frame < this.frames.length){\n      this.set_frame(this.current_frame);\n    }else{\n      var loop_state = this.get_loop_state();\n      if(loop_state == \"loop\"){\n        this.first_frame();\n      }else if(loop_state == \"reflect\"){\n        this.last_frame();\n        this.reverse_animation();\n      }else{\n        this.pause_animation();\n        this.last_frame();\n      }\n    }\n  }\n\n  Animation.prototype.anim_step_reverse = function()\n  {\n    this.current_frame -= 1;\n    if(this.current_frame >= 0){\n      this.set_frame(this.current_frame);\n    }else{\n      var loop_state = this.get_loop_state();\n      if(loop_state == \"loop\"){\n        this.last_frame();\n      }else if(loop_state == \"reflect\"){\n        this.first_frame();\n        this.play_animation();\n      }else{\n        this.pause_animation();\n        this.first_frame();\n      }\n    }\n  }\n\n  Animation.prototype.pause_animation = function()\n  {\n    this.direction = 0;\n    if (this.timer){\n      clearInterval(this.timer);\n      this.timer = null;\n    }\n  }\n\n  Animation.prototype.play_animation = function()\n  {\n    this.pause_animation();\n    this.direction = 1;\n    var t = this;\n    if (!this.timer) this.timer = setInterval(function() {\n        t.anim_step_forward();\n    }, this.interval);\n  }\n\n  Animation.prototype.reverse_animation = function()\n  {\n    this.pause_animation();\n    this.direction = -1;\n    var t = this;\n    if (!this.timer) this.timer = setInterval(function() {\n        t.anim_step_reverse();\n    }, this.interval);\n  }\n</script>\n\n<style>\n.animation {\n    display: inline-block;\n    text-align: center;\n}\ninput[type=range].anim-slider {\n    width: 374px;\n    margin-left: auto;\n    margin-right: auto;\n}\n.anim-buttons {\n    margin: 8px 0px;\n}\n.anim-buttons button {\n    padding: 0;\n    width: 36px;\n}\n.anim-state label {\n    margin-right: 8px;\n}\n.anim-state input {\n    margin: 0;\n    vertical-align: middle;\n}\n</style>\n\n<div class=\"animation\">\n  <img id=\"_anim_imgf8bd6cf5a4614287a418c51d1be5b6b1\">\n  <div class=\"anim-controls\">\n    <input id=\"_anim_sliderf8bd6cf5a4614287a418c51d1be5b6b1\" type=\"range\" class=\"anim-slider\"\n           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n           oninput=\"animf8bd6cf5a4614287a418c51d1be5b6b1.set_frame(parseInt(this.value));\"></input>\n    <div class=\"anim-buttons\">\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.slower()\"><i class=\"fa fa-minus\"></i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.first_frame()\"><i class=\"fa fa-fast-backward\">\n          </i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.previous_frame()\">\n          <i class=\"fa fa-step-backward\"></i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.reverse_animation()\">\n          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.pause_animation()\"><i class=\"fa fa-pause\">\n          </i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.play_animation()\"><i class=\"fa fa-play\"></i>\n          </button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.next_frame()\"><i class=\"fa fa-step-forward\">\n          </i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.last_frame()\"><i class=\"fa fa-fast-forward\">\n          </i></button>\n      <button onclick=\"animf8bd6cf5a4614287a418c51d1be5b6b1.faster()\"><i class=\"fa fa-plus\"></i></button>\n    </div>\n    <form action=\"#n\" name=\"_anim_loop_selectf8bd6cf5a4614287a418c51d1be5b6b1\" class=\"anim-state\">\n      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_f8bd6cf5a4614287a418c51d1be5b6b1\"\n             checked>\n      <label for=\"_anim_radio1_f8bd6cf5a4614287a418c51d1be5b6b1\">Once</label>\n      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_f8bd6cf5a4614287a418c51d1be5b6b1\"\n             >\n      <label for=\"_anim_radio2_f8bd6cf5a4614287a418c51d1be5b6b1\">Loop</label>\n      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_f8bd6cf5a4614287a418c51d1be5b6b1\"\n             >\n      <label for=\"_anim_radio3_f8bd6cf5a4614287a418c51d1be5b6b1\">Reflect</label>\n    </form>\n  </div>\n</div>\n\n\n<script language=\"javascript\">\n  /* Instantiate the Animation class. */\n  /* The IDs given should match those used in the template above. */\n  (function() {\n    var img_id = \"_anim_imgf8bd6cf5a4614287a418c51d1be5b6b1\";\n    var slider_id = \"_anim_sliderf8bd6cf5a4614287a418c51d1be5b6b1\";\n    var loop_select_id = \"_anim_loop_selectf8bd6cf5a4614287a418c51d1be5b6b1\";\n    var frames = new Array(31);\n    \n  frames[0] = 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 frames[15] = 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 frames[19] = 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 frames[23] = 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Kl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\\\n/6+57B9//LF1zPv06SMOHjyocuI6Bw4cEA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 frames[25] = 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Kl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\\\n/6+57B9//LF1zPv06SMOHjyocuI6Bw4cEA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 frames[27] = 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Kl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\\\n/6+57B9//LF1zPv06SMOHjyocuI6Bw4cEA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BERJJiQRMRSYoFTUQkKRY0EZGkWNBERJJiQRMRSYoF\\\nTUQkKRY0EZGk/j9Kn6iMsaEQzAAAAABJRU5ErkJggg==\\\n\"\n\n\n    /* set a timeout to make sure all the above elements are created before\n       the object is initialized. */\n    setTimeout(function() {\n        animf8bd6cf5a4614287a418c51d1be5b6b1 = new Animation(frames, img_id, slider_id, 2000.0,\n                                 loop_select_id);\n    }, 0);\n  })()\n</script>\n"
     },
     "metadata": {},
     "execution_count": 47
    }
   ],
   "source": [
    "from matplotlib import animation \n",
    "from IPython.display import HTML\n",
    "\n",
    "def init():\n",
    "    line.set_data([],[])\n",
    "    return (line,)\n",
    "def animate(i):\n",
    "    state = state_history[i]\n",
    "    x = (state % 3) + 0.5\n",
    "    y = 2.5 - int(state/3)\n",
    "    line.set_data(x,y)\n",
    "    return (line,)\n",
    "anim = animation.FuncAnimation(fig,animate,init_func=init,frames=len(state_history),interval=2000,repeat=False)\n",
    "HTML(anim.to_jshtml())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.    0.5   0.5   0.   ]\n [0.    0.5   0.    0.5  ]\n [0.    0.    0.5   0.5  ]\n [0.333 0.333 0.333 0.   ]\n [0.    0.    0.5   0.5  ]\n [1.    0.    0.    0.   ]\n [1.    0.    0.    0.   ]\n [0.5   0.5   0.    0.   ]]\n[[0, 2], [3, 1], [4, 3], [3, 0], [0, 1], [1, 3], [0, 1], [1, 1], [2, 3], [1, 1], [2, 3], [1, 1], [2, 3], [1, 1], [2, 2], [5, 0], [2, 3], [1, 3], [0, 1], [1, 1], [2, 3], [1, 1], [2, 3], [1, 3], [0, 2], [3, 1], [4, 2], [7, 1], [8, nan]]\n所需步数：28\n"
     ]
    }
   ],
   "source": [
    "def softmax_convert_into_pi_from_theta(theta):\n",
    "    beta = 1.0\n",
    "    [m,n] = theta.shape\n",
    "    pi = np.zeros((m,n))\n",
    "    exp_theta = np.exp(beta*theta)\n",
    "    for i in range(0,m):\n",
    "        pi[i,:] = exp_theta[i,:] / np.nansum(exp_theta[i,:])\n",
    "    pi = np.nan_to_num(pi)\n",
    "    return pi\n",
    "pi_0 = softmax_convert_into_pi_from_theta(theta_0)\n",
    "print(pi_0)\n",
    "\n",
    "# 获取当前动作和下一步的状态\n",
    "def get_action_and_next_s(pi,s):\n",
    "    direction = [\"up\",\"right\",\"down\",\"left\"]\n",
    "    # 根据概率pi[s,:]选择下一步行动\n",
    "    next_direction = np.random.choice(direction, p=pi[s, : ])\n",
    "    if next_direction == \"up\":\n",
    "        action = 0\n",
    "        s_next = s - 3\n",
    "    if next_direction == \"right\":\n",
    "        action = 1\n",
    "        s_next = s + 1\n",
    "    if next_direction == \"down\":\n",
    "        action = 2\n",
    "        s_next = s + 3\n",
    "    if next_direction == \"left\":\n",
    "        action = 3\n",
    "        s_next = s - 1\n",
    "    return [action,s_next]\n",
    "\n",
    "def goal_maze_ret_s_a(pi):\n",
    "    s = 0\n",
    "    s_a_history = [[0,np.nan]] #记录移动位置和动作\n",
    "    while(1):\n",
    "        [action, next_s] = get_action_and_next_s(pi,s)\n",
    "        s_a_history[-1][1] = action\n",
    "        s_a_history.append([next_s,np.nan])\n",
    "        if next_s == 8:\n",
    "            break\n",
    "        else:\n",
    "            s = next_s\n",
    "    return s_a_history\n",
    "s_a_history = goal_maze_ret_s_a(pi_0)\n",
    "print(s_a_history)\n",
    "print(f\"所需步数：{len(s_a_history)-1}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_theta(theta, pi, s_a_history):\n",
    "    eta = 0.1 #学习率\n",
    "    T = len(s_a_history) - 1 # 到达目标需要的步数\n",
    "    [m,n] = theta.shape\n",
    "    delta_theta = theta.copy()\n",
    "    for i in range(0, m):\n",
    "        for j in range(0, n):\n",
    "            if not(np.isnan(theta[i,j])):\n",
    "                SA_i = [SA for SA in s_a_history if SA[0]==i]\n",
    "                SA_ij = [SA for SA in s_a_history if SA == [i,j]]\n",
    "                N_i = len(SA_i) #状态i下动作的总次数\n",
    "                N_ij= len(SA_ij) # 状态i下动作j的总次数\n",
    "                delta_theta[i,j] = (N_ij - pi[i,j]*N_i)/T \n",
    "    new_theta = theta + eta*delta_theta\n",
    "    return new_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "new_theta:[[  nan 0.996 1.004   nan]\n [  nan 1.      nan 1.   ]\n [  nan   nan 1.    1.   ]\n [0.99  1.005 1.005   nan]\n [  nan   nan 0.996 1.004]\n [1.      nan   nan   nan]\n [1.      nan   nan   nan]\n [1.    1.      nan   nan]]\n[[0.    0.498 0.502 0.   ]\n [0.    0.5   0.    0.5  ]\n [0.    0.    0.5   0.5  ]\n [0.33  0.335 0.335 0.   ]\n [0.    0.    0.498 0.502]\n [1.    0.    0.    0.   ]\n [1.    0.    0.    0.   ]\n [0.5   0.5   0.    0.   ]]\n"
     ]
    }
   ],
   "source": [
    "new_theta = update_theta(theta_0, pi_0, s_a_history)\n",
    "print(f\"new_theta:{new_theta}\")\n",
    "pi = softmax_convert_into_pi_from_theta(new_theta)\n",
    "print(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
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      "求解迷宫需要的步数：4\n",
      "0.0001515088852513495\n",
      "求解迷宫需要的步数：4\n",
      "0.0001512242829846619\n",
      "求解迷宫需要的步数：4\n",
      "0.00015094048892044971\n",
      "求解迷宫需要的步数：4\n",
      "0.00015065749997240918\n",
      "求解迷宫需要的步数：4\n",
      "0.00015037531306986117\n",
      "求解迷宫需要的步数：4\n",
      "0.00015009392515618301\n",
      "求解迷宫需要的步数：4\n",
      "0.0001498133331894573\n",
      "求解迷宫需要的步数：4\n",
      "0.0001495335341428431\n",
      "求解迷宫需要的步数：4\n",
      "0.00014925452500281003\n",
      "求解迷宫需要的步数：4\n",
      "0.0001489763027724758\n",
      "求解迷宫需要的步数：4\n",
      "0.00014869886446635013\n",
      "求解迷宫需要的步数：4\n",
      "0.00014842220711645468\n",
      "求解迷宫需要的步数：4\n",
      "0.00014814632776588045\n",
      "求解迷宫需要的步数：4\n",
      "0.00014787122347393808\n",
      "求解迷宫需要的步数：4\n",
      "0.0001475968913131117\n",
      "求解迷宫需要的步数：4\n",
      "0.000147323328370157\n",
      "求解迷宫需要的步数：4\n",
      "0.00014705053174569188\n",
      "求解迷宫需要的步数：4\n",
      "0.00014677849855341749\n",
      "求解迷宫需要的步数：4\n",
      "0.00014650722592123196\n",
      "求解迷宫需要的步数：4\n",
      "0.00014623671099090602\n",
      "求解迷宫需要的步数：4\n",
      "0.00014596695091787133\n",
      "求解迷宫需要的步数：4\n",
      "0.00014569794286977203\n",
      "求解迷宫需要的步数：4\n",
      "0.00014542968402921075\n",
      "求解迷宫需要的步数：4\n",
      "0.0001451621715910685\n",
      "求解迷宫需要的步数：4\n",
      "0.00014489540276378318\n",
      "求解迷宫需要的步数：4\n",
      "0.0001446293747693339\n",
      "求解迷宫需要的步数：4\n",
      "0.0011713643579607282\n",
      "求解迷宫需要的步数：6\n",
      "0.00014611906303040392\n",
      "求解迷宫需要的步数：4\n",
      "0.00014584987140766302\n",
      "求解迷宫需要的步数：4\n",
      "0.0001455814286337436\n",
      "求解迷宫需要的步数：4\n",
      "0.00014531373191006836\n",
      "求解迷宫需要的步数：4\n",
      "0.00014504677845357528\n",
      "求解迷宫需要的步数：4\n",
      "0.00014478056549200105\n",
      "求解迷宫需要的步数：4\n",
      "0.0001445150902677321\n",
      "求解迷宫需要的步数：4\n",
      "0.0001442503500346439\n",
      "求解迷宫需要的步数：4\n",
      "0.00014398634206089743\n",
      "求解迷宫需要的步数：4\n",
      "0.00014372306362618777\n",
      "求解迷宫需要的步数：4\n",
      "0.0001434605120249656\n",
      "求解迷宫需要的步数：4\n",
      "0.00014319868456059807\n",
      "求解迷宫需要的步数：4\n",
      "0.00014293757855259742\n",
      "求解迷宫需要的步数：4\n",
      "0.00014267719133259117\n",
      "求解迷宫需要的步数：4\n",
      "0.0001424175202419109\n",
      "求解迷宫需要的步数：4\n",
      "0.00014215856263668364\n",
      "求解迷宫需要的步数：4\n",
      "0.00014190031588555592\n",
      "求解迷宫需要的步数：4\n",
      "0.00014164277736754098\n",
      "求解迷宫需要的步数：4\n",
      "0.00014138594447527138\n",
      "求解迷宫需要的步数：4\n",
      "0.00014112981461310292\n",
      "求解迷宫需要的步数：4\n",
      "0.00014087438519678162\n",
      "求解迷宫需要的步数：4\n",
      "0.00014061965365533106\n",
      "求解迷宫需要的步数：4\n",
      "0.004148030391337546\n",
      "求解迷宫需要的步数：6\n",
      "0.00014212145691936198\n",
      "求解迷宫需要的步数：4\n",
      "0.00014186368152915158\n",
      "求解迷宫需要的步数：4\n",
      "0.00014160661117713393\n",
      "求解迷宫需要的步数：4\n",
      "0.00014135024327650673\n",
      "求解迷宫需要的步数：4\n",
      "0.00014109457525438365\n",
      "求解迷宫需要的步数：4\n",
      "0.00014083960454686247\n",
      "求解迷宫需要的步数：4\n",
      "0.0001405853286043958\n",
      "求解迷宫需要的步数：4\n",
      "0.00014033174488893574\n",
      "求解迷宫需要的步数：4\n",
      "0.00014007885087176548\n",
      "求解迷宫需要的步数：4\n",
      "0.00013982664403865488\n",
      "求解迷宫需要的步数：4\n",
      "0.00013957512188523223\n",
      "求解迷宫需要的步数：4\n",
      "0.00013932428191867213\n",
      "求解迷宫需要的步数：4\n",
      "0.0001390741216586583\n",
      "求解迷宫需要的步数：4\n",
      "0.00013882463863483692\n",
      "求解迷宫需要的步数：4\n",
      "0.00013857583038866944\n",
      "求解迷宫需要的步数：4\n",
      "0.00013832769447404657\n",
      "求解迷宫需要的步数：4\n",
      "0.00013808022845269476\n",
      "求解迷宫需要的步数：4\n",
      "0.00013783342990229645\n",
      "求解迷宫需要的步数：4\n",
      "0.001056516255330998\n",
      "求解迷宫需要的步数：6\n",
      "0.00013877828461897855\n",
      "求解迷宫需要的步数：4\n",
      "0.0001385303333642108\n",
      "求解迷宫需要的步数：4\n",
      "0.00013828304912735963\n",
      "求解迷宫需要的步数：4\n",
      "0.00013803642950575325\n",
      "求解迷宫需要的步数：4\n",
      "0.00013779047210591734\n",
      "求解迷宫需要的步数：4\n",
      "0.0001375451745466525\n",
      "求解迷宫需要的步数：4\n",
      "0.0001373005344556949\n",
      "求解迷宫需要的步数：4\n",
      "0.00013705654947369222\n",
      "求解迷宫需要的步数：4\n",
      "0.00013681321724974202\n",
      "求解迷宫需要的步数：4\n",
      "0.013352786494196203\n",
      "求解迷宫需要的步数：16\n",
      "0.0001372287417594157\n",
      "求解迷宫需要的步数：4\n",
      "0.00013698504663945538\n",
      "求解迷宫需要的步数：4\n",
      "0.00013674200284641454\n",
      "求解迷宫需要的步数：4\n",
      "0.00013649960804843278\n",
      "求解迷宫需要的步数：4\n",
      "0.00013625785992626635\n",
      "求解迷宫需要的步数：4\n",
      "0.00013601675616879694\n",
      "求解迷宫需要的步数：4\n",
      "0.00013577629447755063\n",
      "求解迷宫需要的步数：4\n",
      "0.00013553647256225008\n",
      "求解迷宫需要的步数：4\n",
      "0.00013529728814446786\n",
      "求解迷宫需要的步数：4\n",
      "0.00013505873895476583\n",
      "求解迷宫需要的步数：4\n",
      "0.00013482082273456875\n",
      "求解迷宫需要的步数：4\n",
      "0.00013458353723519619\n",
      "求解迷宫需要的步数：4\n",
      "0.0001343468802183414\n",
      "求解迷宫需要的步数：4\n",
      "0.00013411084945487255\n",
      "求解迷宫需要的步数：4\n",
      "0.00013387544272591353\n",
      "求解迷宫需要的步数：4\n",
      "0.00013364065782292718\n",
      "求解迷宫需要的步数：4\n",
      "0.00013340649254713413\n",
      "求解迷宫需要的步数：4\n",
      "0.00013317294470892999\n",
      "求解迷宫需要的步数：4\n",
      "0.0001329400121281802\n",
      "求解迷宫需要的步数：4\n",
      "0.00013270769263566684\n",
      "求解迷宫需要的步数：4\n",
      "0.00013247598407110928\n",
      "求解迷宫需要的步数：4\n",
      "0.00013224488428287794\n",
      "求解迷宫需要的步数：4\n",
      "0.00013201439113107172\n",
      "求解迷宫需要的步数：4\n",
      "0.00013178450248288627\n",
      "求解迷宫需要的步数：4\n",
      "0.00013155521621548497\n",
      "求解迷宫需要的步数：4\n",
      "0.00013132653021779433\n",
      "求解迷宫需要的步数：4\n",
      "0.00013109844238377855\n",
      "求解迷宫需要的步数：4\n",
      "0.0001308709506203428\n",
      "求解迷宫需要的步数：4\n",
      "0.0001306440528420303\n",
      "求解迷宫需要的步数：4\n",
      "0.00013041774697218102\n",
      "求解迷宫需要的步数：4\n",
      "0.005165282107778281\n",
      "求解迷宫需要的步数：10\n",
      "0.00013122940770030414\n",
      "求解迷宫需要的步数：4\n",
      "0.00013100168234623198\n",
      "求解迷宫需要的步数：4\n",
      "0.0001307745513422151\n",
      "求解迷宫需要的步数：4\n",
      "0.00013054801261189533\n",
      "求解迷宫需要的步数：4\n",
      "0.0001303220640901017\n",
      "求解迷宫需要的步数：4\n",
      "0.00013009670371844258\n",
      "求解迷宫需要的步数：4\n",
      "0.00012987192944878719\n",
      "求解迷宫需要的步数：4\n",
      "0.00012964773924224564\n",
      "求解迷宫需要的步数：4\n",
      "0.00012942413106781236\n",
      "求解迷宫需要的步数：4\n",
      "0.0011118506208425156\n",
      "求解迷宫需要的步数：6\n",
      "0.00013078677920195375\n",
      "求解迷宫需要的步数：4\n",
      "0.00013056036625307826\n",
      "求解迷宫需要的步数：4\n",
      "0.00013033454246063995\n",
      "求解迷宫需要的步数：4\n",
      "0.00013010930577423904\n",
      "求解迷宫需要的步数：4\n",
      "0.00012988465415352674\n",
      "求解迷宫需要的步数：4\n",
      "0.00012966058556543314\n",
      "求解迷宫需要的步数：4\n",
      "0.00012943709798833233\n",
      "求解迷宫需要的步数：4\n",
      "0.00012921418940733606\n",
      "求解迷宫需要的步数：4\n",
      "0.00012899185781627305\n",
      "求解迷宫需要的步数：4\n",
      "0.0011276162724346145\n",
      "求解迷宫需要的步数：6\n",
      "0.00013041271528754263\n",
      "求解迷宫需要的步数：4\n",
      "0.00013018736362974473\n",
      "求解迷宫需要的步数：4\n",
      "0.0001299625970508072\n",
      "求解迷宫需要的步数：4\n",
      "0.0001297384135191485\n",
      "求解迷宫需要的步数：4\n",
      "0.00012951481101478556\n",
      "求解迷宫需要的步数：4\n",
      "0.00012929178752516673\n",
      "求解迷宫需要的步数：4\n",
      "0.00012906934104627704\n",
      "求解迷宫需要的步数：4\n",
      "0.0001288474695834499\n",
      "求解迷宫需要的步数：4\n",
      "0.00012862617115081895\n",
      "求解迷宫需要的步数：4\n",
      "0.00012840544377019925\n",
      "求解迷宫需要的步数：4\n",
      "0.00012818528547265187\n",
      "求解迷宫需要的步数：4\n",
      "0.0001279656942976895\n",
      "求解迷宫需要的步数：4\n",
      "0.0001277466682926484\n",
      "求解迷宫需要的步数：4\n",
      "0.00012752820551473025\n",
      "求解迷宫需要的步数：4\n",
      "0.00012731030402736432\n",
      "求解迷宫需要的步数：4\n",
      "0.00012709296190487052\n",
      "求解迷宫需要的步数：4\n",
      "0.00012687617722779466\n",
      "求解迷宫需要的步数：4\n",
      "0.00012665994808525732\n",
      "求解迷宫需要的步数：4\n",
      "0.0001264442725758888\n",
      "求解迷宫需要的步数：4\n",
      "0.0001262291488048871\n",
      "求解迷宫需要的步数：4\n",
      "0.0001260145748865106\n",
      "求解迷宫需要的步数：4\n",
      "0.00012580054894294028\n",
      "求解迷宫需要的步数：4\n",
      "0.00012558706910390828\n",
      "求解迷宫需要的步数：4\n",
      "0.00012537413350785162\n",
      "求解迷宫需要的步数：4\n",
      "0.00012516174030077244\n",
      "求解迷宫需要的步数：4\n",
      "0.00012494988763640108\n",
      "求解迷宫需要的步数：4\n",
      "0.00012473857367693332\n",
      "求解迷宫需要的步数：4\n",
      "0.0001245277965918317\n",
      "求解迷宫需要的步数：4\n",
      "0.00012431755455866687\n",
      "求解迷宫需要的步数：4\n",
      "0.00012410784576256245\n",
      "求解迷宫需要的步数：4\n",
      "0.0001238986683962176\n",
      "求解迷宫需要的步数：4\n",
      "0.00012369002066090796\n",
      "求解迷宫需要的步数：4\n",
      "0.004138430475908592\n",
      "求解迷宫需要的步数：6\n",
      "0.00012515483908368853\n",
      "求解迷宫需要的步数：4\n",
      "0.0001249431281503989\n",
      "求解迷宫需要的步数：4\n",
      "0.0001247319549270605\n",
      "求解迷宫需要的步数：4\n",
      "0.0001245213175887199\n",
      "求解迷宫需要的步数：4\n",
      "0.00012431121431953455\n",
      "求解迷宫需要的步数：4\n",
      "0.00012410164331201103\n",
      "求解迷宫需要的步数：4\n",
      "0.00012389260276528778\n",
      "求解迷宫需要的步数：4\n",
      "0.00012368409088624015\n",
      "求解迷宫需要的步数：4\n",
      "0.0001234761058905732\n",
      "求解迷宫需要的步数：4\n",
      "0.00012326864599917706\n",
      "求解迷宫需要的步数：4\n",
      "0.0001230617094429374\n",
      "求解迷宫需要的步数：4\n",
      "0.00012285529445862572\n",
      "求解迷宫需要的步数：4\n",
      "0.00012264939929067936\n",
      "求解迷宫需要的步数：4\n",
      "0.00012244402219176512\n",
      "求解迷宫需要的步数：4\n",
      "0.00012223916142110533\n",
      "求解迷宫需要的步数：4\n",
      "0.0001220348152456592\n",
      "求解迷宫需要的步数：4\n",
      "0.00012183098193829095\n",
      "求解迷宫需要的步数：4\n",
      "0.00012162765978224188\n",
      "求解迷宫需要的步数：4\n",
      "0.0001214248470643043\n",
      "求解迷宫需要的步数：4\n",
      "0.00012122254208116537\n",
      "求解迷宫需要的步数：4\n",
      "0.00012102074313504428\n",
      "求解迷宫需要的步数：4\n",
      "0.00012081944853603414\n",
      "求解迷宫需要的步数：4\n",
      "0.00012061865660202217\n",
      "求解迷宫需要的步数：4\n",
      "0.00012041836565484729\n",
      "求解迷宫需要的步数：4\n",
      "0.00012021857402743502\n",
      "求解迷宫需要的步数：4\n",
      "0.00012001928005743283\n",
      "求解迷宫需要的步数：4\n",
      "0.00011982048208938369\n",
      "求解迷宫需要的步数：4\n",
      "0.00011962217847475906\n",
      "求解迷宫需要的步数：4\n",
      "0.00011942436757283147\n",
      "求解迷宫需要的步数：4\n",
      "0.004112024344958895\n",
      "求解迷宫需要的步数：6\n",
      "0.00012093314361431157\n",
      "求解迷宫需要的步数：4\n",
      "0.00012073207549975588\n",
      "求解迷宫需要的步数：4\n",
      "0.00012053150916951048\n",
      "求解迷宫需要的步数：4\n",
      "0.004111484361768426\n",
      "求解迷宫需要的步数：6\n",
      "0.00012214215358113956\n",
      "求解迷宫需要的步数：4\n",
      "0.00012193795228684391\n",
      "求解迷宫需要的步数：4\n",
      "0.00012173426350066234\n",
      "求解迷宫需要的步数：4\n",
      "0.00012153108550439981\n",
      "求解迷宫需要的步数：4\n",
      "0.0001213284165902627\n",
      "求解迷宫需要的步数：4\n",
      "0.00012112625505398752\n",
      "求解迷宫需要的步数：4\n",
      "0.00012092459920083794\n",
      "求解迷宫需要的步数：4\n",
      "0.00012072344734209012\n",
      "求解迷宫需要的步数：4\n",
      "0.00012052279779693059\n",
      "求解迷宫需要的步数：4\n",
      "0.00012032264889057925\n",
      "求解迷宫需要的步数：4\n",
      "0.00012012299895589051\n",
      "求解迷宫需要的步数：4\n",
      "0.00011992384633202624\n",
      "求解迷宫需要的步数：4\n",
      "0.00011972518936636221\n",
      "求解迷宫需要的步数：4\n",
      "0.00011952702641179237\n",
      "求解迷宫需要的步数：4\n",
      "0.00011932935582865088\n",
      "求解迷宫需要的步数：4\n",
      "0.0001191321759833816\n",
      "求解迷宫需要的步数：4\n",
      "0.000981823219200248\n",
      "求解迷宫需要的步数：6\n",
      "0.00011999495050902913\n",
      "求解迷宫需要的步数：4\n",
      "0.00011979666668159375\n",
      "求解迷宫需要的步数：4\n",
      "0.00011959887410574292\n",
      "求解迷宫需要的步数：4\n",
      "0.00011940157115843467\n",
      "求解迷宫需要的步数：4\n",
      "0.0001192047562225268\n",
      "求解迷宫需要的步数：4\n",
      "0.00011900842768929228\n",
      "求解迷宫需要的步数：4\n",
      "0.00011881258395482659\n",
      "求解迷宫需要的步数：4\n",
      "0.00011861722342310262\n",
      "求解迷宫需要的步数：4\n",
      "0.00011842234450426536\n",
      "求解迷宫需要的步数：4\n",
      "0.00011822794561471006\n",
      "求解迷宫需要的步数：4\n",
      "0.00011803402517789573\n",
      "求解迷宫需要的步数：4\n",
      "0.00011784058162337026\n",
      "求解迷宫需要的步数：4\n",
      "0.0011464361644034672\n",
      "求解迷宫需要的步数：6\n",
      "0.00011936239685829582\n",
      "求解迷宫需要的步数：4\n",
      "0.00011916570921068938\n",
      "求解迷宫需要的步数：4\n",
      "0.00011896950732450881\n",
      "求解迷宫需要的步数：4\n",
      "0.00011877378960004417\n",
      "求解迷宫需要的步数：4\n",
      "0.00011857855444488176\n",
      "求解迷宫需要的步数：4\n",
      "0.00011838380027298125\n",
      "求解迷宫需要的步数：4\n",
      "0.0001181895255049064\n",
      "求解迷宫需要的步数：4\n",
      "0.00011799572856776089\n",
      "求解迷宫需要的步数：4\n",
      "0.0001178024078943643\n",
      "求解迷宫需要的步数：4\n",
      "0.00011760956192533728\n",
      "求解迷宫需要的步数：4\n",
      "0.0011648698295269617\n",
      "求解迷宫需要的步数：6\n",
      "0.00011919788780174502\n",
      "求解迷宫需要的步数：4\n",
      "0.00011900155293352935\n",
      "求解迷宫需要的步数：4\n",
      "0.0001188057027144869\n",
      "求解迷宫需要的步数：4\n",
      "0.00011861033555207387\n",
      "求解迷宫需要的步数：4\n",
      "0.0001184154498570858\n",
      "求解迷宫需要的步数：4\n",
      "0.00011822104404846621\n",
      "求解迷宫需要的步数：4\n",
      "0.00121684841802841\n",
      "求解迷宫需要的步数：6\n",
      "0.00011994190329209752\n",
      "求解迷宫需要的步数：4\n",
      "0.0001197433843403619\n",
      "求解迷宫需要的步数：4\n",
      "0.00011954535833868206\n",
      "求解迷宫需要的步数：4\n",
      "0.00011934782365308552\n",
      "求解迷宫需要的步数：4\n",
      "0.00011915077865850589\n",
      "求解迷宫需要的步数：4\n",
      "0.00011895422173489358\n",
      "求解迷宫需要的步数：4\n",
      "0.00011875815126989771\n",
      "求解迷宫需要的步数：4\n",
      "0.00011856256565653811\n",
      "求解迷宫需要的步数：4\n",
      "0.00011836746329658109\n",
      "求解迷宫需要的步数：4\n",
      "0.0001181728425958227\n",
      "求解迷宫需要的步数：4\n",
      "0.00011797870196911427\n",
      "求解迷宫需要的步数：4\n",
      "0.0001177850398361574\n",
      "求解迷宫需要的步数：4\n",
      "0.00011759185462312943\n",
      "求解迷宫需要的步数：4\n",
      "0.00011739914476439212\n",
      "求解迷宫需要的步数：4\n",
      "0.00011720690869855034\n",
      "求解迷宫需要的步数：4\n",
      "0.00011701514487217832\n",
      "求解迷宫需要的步数：4\n",
      "0.0001168238517376425\n",
      "求解迷宫需要的步数：4\n",
      "0.00011663302775317616\n",
      "求解迷宫需要的步数：4\n",
      "0.00011644267138477549\n",
      "求解迷宫需要的步数：4\n",
      "0.00011625278110329734\n",
      "求解迷宫需要的步数：4\n",
      "0.00011606335538616105\n",
      "求解迷宫需要的步数：4\n",
      "0.00011587439271718361\n",
      "求解迷宫需要的步数：4\n",
      "0.00011568589158665772\n",
      "求解迷宫需要的步数：4\n",
      "0.00011549785049036997\n",
      "求解迷宫需要的步数：4\n",
      "0.00011531026793140664\n",
      "求解迷宫需要的步数：4\n",
      "0.00011512314241675196\n",
      "求解迷宫需要的步数：4\n",
      "0.00011493647246201347\n",
      "求解迷宫需要的步数：4\n",
      "0.0001147502565881451\n",
      "求解迷宫需要的步数：4\n",
      "0.00011456449331957719\n",
      "求解迷宫需要的步数：4\n",
      "0.00011437918119073208\n",
      "求解迷宫需要的步数：4\n",
      "0.00011419431873969238\n",
      "求解迷宫需要的步数：4\n",
      "0.00011400990450974313\n",
      "求解迷宫需要的步数：4\n",
      "0.00011382593705247003\n",
      "求解迷宫需要的步数：4\n",
      "0.00011364241492308261\n",
      "求解迷宫需要的步数：4\n",
      "0.00011345933668401552\n",
      "求解迷宫需要的步数：4\n",
      "0.00011327670090259707\n",
      "求解迷宫需要的步数：4\n",
      "0.00011309450615305978\n",
      "求解迷宫需要的步数：4\n",
      "0.00011291275101405103\n",
      "求解迷宫需要的步数：4\n",
      "0.00011273143407031748\n",
      "求解迷宫需要的步数：4\n",
      "0.00011255055391366092\n",
      "求解迷宫需要的步数：4\n",
      "0.00011237010913970648\n",
      "求解迷宫需要的步数：4\n",
      "0.00011219009835003284\n",
      "求解迷宫需要的步数：4\n",
      "0.00011201052015345422\n",
      "求解迷宫需要的步数：4\n",
      "0.00011183137316202359\n",
      "求解迷宫需要的步数：4\n",
      "0.0001116526559955533\n",
      "求解迷宫需要的步数：4\n",
      "0.000960243406622369\n",
      "求解迷宫需要的步数：6\n",
      "0.00011250161408740342\n",
      "求解迷宫需要的步数：4\n",
      "0.00011232176575687834\n",
      "求解迷宫需要的步数：4\n",
      "0.00011214234819992286\n",
      "求解迷宫需要的步数：4\n",
      "0.00011196336004153269\n",
      "求解迷宫需要的步数：4\n",
      "0.00011178479991311163\n",
      "求解迷宫需要的步数：4\n",
      "0.0001116066664490923\n",
      "求解迷宫需要的步数：4\n",
      "0.00011142895829178122\n",
      "求解迷宫需要的步数：4\n",
      "0.00011125167408680692\n",
      "求解迷宫需要的步数：4\n",
      "0.00011107481248716702\n",
      "求解迷宫需要的步数：4\n",
      "0.00011089837214998087\n",
      "求解迷宫需要的步数：4\n",
      "0.00011072235173760839\n",
      "求解迷宫需要的步数：4\n",
      "0.00011054674991847757\n",
      "求解迷宫需要的步数：4\n",
      "0.0001103715653658667\n",
      "求解迷宫需要的步数：4\n",
      "0.00011019679675772567\n",
      "求解迷宫需要的步数：4\n",
      "0.00011002244277879408\n",
      "求解迷宫需要的步数：4\n",
      "0.00010984850211722894\n",
      "求解迷宫需要的步数：4\n",
      "0.00010967497346827011\n",
      "求解迷宫需要的步数：4\n",
      "0.00010950185553025744\n",
      "求解迷宫需要的步数：4\n",
      "0.00010932914700783475\n",
      "求解迷宫需要的步数：4\n",
      "0.00010915684661091593\n",
      "求解迷宫需要的步数：4\n",
      "0.0001089849530537361\n",
      "求解迷宫需要的步数：4\n",
      "0.00010881346505652208\n",
      "求解迷宫需要的步数：4\n",
      "0.0001086423813441862\n",
      "求解迷宫需要的步数：4\n",
      "0.00010847170064532535\n",
      "求解迷宫需要的步数：4\n",
      "0.00010830142169538509\n",
      "求解迷宫需要的步数：4\n",
      "0.00010813154323493362\n",
      "求解迷宫需要的步数：4\n",
      "0.00010796206400682726\n",
      "求解迷宫需要的步数：4\n",
      "0.00010779298276252999\n",
      "求解迷宫需要的步数：4\n",
      "0.00010762429825506709\n",
      "求解迷宫需要的步数：4\n",
      "0.00010745600924468024\n",
      "求解迷宫需要的步数：4\n",
      "0.00010728811449526622\n",
      "求解迷宫需要的步数：4\n",
      "0.0001071206127753084\n",
      "求解迷宫需要的步数：4\n",
      "0.00010695350285929404\n",
      "求解迷宫需要的步数：4\n",
      "0.00010678678352625884\n",
      "求解迷宫需要的步数：4\n",
      "0.00010662045355834884\n",
      "求解迷宫需要的步数：4\n",
      "0.00010645451174410604\n",
      "求解迷宫需要的步数：4\n",
      "0.00010628895687683944\n",
      "求解迷宫需要的步数：4\n",
      "0.0001061237877537178\n",
      "求解迷宫需要的步数：4\n",
      "0.00010595900317669597\n",
      "求解迷宫需要的步数：4\n",
      "0.00010579460195303536\n",
      "求解迷宫需要的步数：4\n",
      "0.00010563058289350495\n",
      "求解迷宫需要的步数：4\n",
      "0.00010546694481532344\n",
      "求解迷宫需要的步数：4\n",
      "0.00010530368653774956\n",
      "求解迷宫需要的步数：4\n",
      "0.003991979631250286\n",
      "求解迷宫需要的步数：6\n",
      "0.00010669411553537907\n",
      "求解迷宫需要的步数：4\n",
      "0.00010652793916031411\n",
      "求解迷宫需要的步数：4\n",
      "0.00010636215060313634\n",
      "求解迷宫需要的步数：4\n",
      "0.00010619674865765955\n",
      "求解迷宫需要的步数：4\n",
      "0.00010603173212244722\n",
      "求解迷宫需要的步数：4\n",
      "0.00010586709979984975\n",
      "求解迷宫需要的步数：4\n",
      "0.00010570285049772005\n",
      "求解迷宫需要的步数：4\n",
      "0.0001055389830296842\n",
      "求解迷宫需要的步数：4\n",
      "0.00010537549621125394\n",
      "求解迷宫需要的步数：4\n",
      "0.00010521238886473418\n",
      "求解迷宫需要的步数：4\n",
      "0.0001050496598161213\n",
      "求解迷宫需要的步数：4\n",
      "0.00010488730789563923\n",
      "求解迷宫需要的步数：4\n",
      "0.00010472533193948627\n",
      "求解迷宫需要的步数：4\n",
      "0.00010456373078591985\n",
      "求解迷宫需要的步数：4\n",
      "0.00010440250328027853\n",
      "求解迷宫需要的步数：4\n",
      "0.003980473020653231\n",
      "求解迷宫需要的步数：6\n",
      "0.00010586076827211188\n",
      "求解迷宫需要的步数：4\n",
      "0.00010569637599217724\n",
      "求解迷宫需要的步数：4\n",
      "0.00010553236643176533\n",
      "求解迷宫需要的步数：4\n",
      "0.00010536873840324285\n",
      "求解迷宫需要的步数：4\n",
      "0.00010520549072236957\n",
      "求解迷宫需要的步数：4\n",
      "0.00010504262221035059\n",
      "求解迷宫需要的步数：4\n",
      "0.00010488013169398028\n",
      "求解迷宫需要的步数：4\n",
      "0.00010471801800299337\n",
      "求解迷宫需要的步数：4\n",
      "0.00010455627997157935\n",
      "求解迷宫需要的步数：4\n",
      "0.00010439491643999751\n",
      "求解迷宫需要的步数：4\n",
      "0.00010423392625141456\n",
      "求解迷宫需要的步数：4\n",
      "0.0001040733082546437\n",
      "求解迷宫需要的步数：4\n",
      "0.00010391306130205259\n",
      "求解迷宫需要的步数：4\n",
      "0.00010375318425077593\n",
      "求解迷宫需要的步数：4\n",
      "0.00010359367596285592\n",
      "求解迷宫需要的步数：4\n",
      "0.00010343453530334452\n",
      "求解迷宫需要的步数：4\n",
      "0.00010327576114352657\n",
      "求解迷宫需要的步数：4\n",
      "0.00010311735235703744\n",
      "求解迷宫需要的步数：4\n",
      "0.00010295930782378351\n",
      "求解迷宫需要的步数：4\n",
      "0.000102801626425994\n",
      "求解迷宫需要的步数：4\n",
      "0.00010264430705238595\n",
      "求解迷宫需要的步数：4\n",
      "0.00010248734859377023\n",
      "求解迷宫需要的步数：4\n",
      "0.00010233074994667885\n",
      "求解迷宫需要的步数：4\n",
      "0.00010217451001096577\n",
      "求解迷宫需要的步数：4\n",
      "0.00010201862769144109\n",
      "求解迷宫需要的步数：4\n",
      "0.00010186310189681455\n",
      "求解迷宫需要的步数：4\n",
      "0.00010170793153919944\n",
      "求解迷宫需要的步数：4\n",
      "0.00010155311553639718\n",
      "求解迷宫需要的步数：4\n",
      "0.00010139865280918946\n",
      "求解迷宫需要的步数：4\n",
      "0.0001012445422823513\n",
      "求解迷宫需要的步数：4\n",
      "0.00010109078288560863\n",
      "求解迷宫需要的步数：4\n",
      "0.00010093737355204233\n",
      "求解迷宫需要的步数：4\n",
      "0.00010078431321957661\n",
      "求解迷宫需要的步数：4\n",
      "0.0001006316008287534\n",
      "求解迷宫需要的步数：4\n",
      "0.00010047923532550788\n",
      "求解迷宫需要的步数：4\n",
      "0.00010032721565964194\n",
      "求解迷宫需要的步数：4\n",
      "0.00010017554078348839\n",
      "求解迷宫需要的步数：4\n",
      "0.00010002420965527642\n",
      "求解迷宫需要的步数：4\n",
      "9.987322123637676e-05\n",
      "求解迷宫需要的步数：4\n",
      "[[0.    0.016 0.984 0.   ]\n",
      " [0.    0.237 0.    0.763]\n",
      " [0.    0.    0.467 0.533]\n",
      " [0.009 0.98  0.012 0.   ]\n",
      " [0.    0.    0.987 0.013]\n",
      " [1.    0.    0.    0.   ]\n",
      " [1.    0.    0.    0.   ]\n",
      " [0.016 0.984 0.    0.   ]]\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ],
      "text/html": "\n<link rel=\"stylesheet\"\nhref=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\ncss/font-awesome.min.css\">\n<script language=\"javascript\">\n  function isInternetExplorer() {\n    ua = navigator.userAgent;\n    /* MSIE used to detect old browsers and Trident used to newer ones*/\n    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n  }\n\n  /* Define the Animation class */\n  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n    this.img_id = img_id;\n    this.slider_id = slider_id;\n    this.loop_select_id = loop_select_id;\n    this.interval = interval;\n    this.current_frame = 0;\n    this.direction = 0;\n    this.timer = null;\n    this.frames = new Array(frames.length);\n\n    for (var i=0; i<frames.length; i++)\n    {\n     this.frames[i] = new Image();\n     this.frames[i].src = frames[i];\n    }\n    var slider = document.getElementById(this.slider_id);\n    slider.max = this.frames.length - 1;\n    if (isInternetExplorer()) {\n        // switch from oninput to onchange because IE <= 11 does not conform\n        // with W3C specification. It ignores oninput and onchange behaves\n        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n        slider.setAttribute('oninput', null);\n    }\n    this.set_frame(this.current_frame);\n  }\n\n  Animation.prototype.get_loop_state = function(){\n    var button_group = document[this.loop_select_id].state;\n    for (var i = 0; i < button_group.length; i++) {\n        var button = button_group[i];\n        if (button.checked) {\n            return button.value;\n        }\n    }\n    return undefined;\n  }\n\n  Animation.prototype.set_frame = function(frame){\n    this.current_frame = frame;\n    document.getElementById(this.img_id).src =\n            this.frames[this.current_frame].src;\n    document.getElementById(this.slider_id).value = this.current_frame;\n  }\n\n  Animation.prototype.next_frame = function()\n  {\n    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n  }\n\n  Animation.prototype.previous_frame = function()\n  {\n    this.set_frame(Math.max(0, this.current_frame - 1));\n  }\n\n  Animation.prototype.first_frame = function()\n  {\n    this.set_frame(0);\n  }\n\n  Animation.prototype.last_frame = function()\n  {\n    this.set_frame(this.frames.length - 1);\n  }\n\n  Animation.prototype.slower = function()\n  {\n    this.interval /= 0.7;\n    if(this.direction > 0){this.play_animation();}\n    else if(this.direction < 0){this.reverse_animation();}\n  }\n\n  Animation.prototype.faster = function()\n  {\n    this.interval *= 0.7;\n    if(this.direction > 0){this.play_animation();}\n    else if(this.direction < 0){this.reverse_animation();}\n  }\n\n  Animation.prototype.anim_step_forward = function()\n  {\n    this.current_frame += 1;\n    if(this.current_frame < this.frames.length){\n      this.set_frame(this.current_frame);\n    }else{\n      var loop_state = this.get_loop_state();\n      if(loop_state == \"loop\"){\n        this.first_frame();\n      }else if(loop_state == \"reflect\"){\n        this.last_frame();\n        this.reverse_animation();\n      }else{\n        this.pause_animation();\n        this.last_frame();\n      }\n    }\n  }\n\n  Animation.prototype.anim_step_reverse = function()\n  {\n    this.current_frame -= 1;\n    if(this.current_frame >= 0){\n      this.set_frame(this.current_frame);\n    }else{\n      var loop_state = this.get_loop_state();\n      if(loop_state == \"loop\"){\n        this.last_frame();\n      }else if(loop_state == \"reflect\"){\n        this.first_frame();\n        this.play_animation();\n      }else{\n        this.pause_animation();\n        this.first_frame();\n      }\n    }\n  }\n\n  Animation.prototype.pause_animation = function()\n  {\n    this.direction = 0;\n    if (this.timer){\n      clearInterval(this.timer);\n      this.timer = null;\n    }\n  }\n\n  Animation.prototype.play_animation = function()\n  {\n    this.pause_animation();\n    this.direction = 1;\n    var t = this;\n    if (!this.timer) this.timer = setInterval(function() {\n        t.anim_step_forward();\n    }, this.interval);\n  }\n\n  Animation.prototype.reverse_animation = function()\n  {\n    this.pause_animation();\n    this.direction = -1;\n    var t = this;\n    if (!this.timer) this.timer = setInterval(function() {\n        t.anim_step_reverse();\n    }, this.interval);\n  }\n</script>\n\n<style>\n.animation {\n    display: inline-block;\n    text-align: center;\n}\ninput[type=range].anim-slider {\n    width: 374px;\n    margin-left: auto;\n    margin-right: auto;\n}\n.anim-buttons {\n    margin: 8px 0px;\n}\n.anim-buttons button {\n    padding: 0;\n    width: 36px;\n}\n.anim-state label {\n    margin-right: 8px;\n}\n.anim-state input {\n    margin: 0;\n    vertical-align: middle;\n}\n</style>\n\n<div class=\"animation\">\n  <img id=\"_anim_imgb1a36cca1fda41c7aef4a6f3b1a3ba14\">\n  <div class=\"anim-controls\">\n    <input id=\"_anim_sliderb1a36cca1fda41c7aef4a6f3b1a3ba14\" type=\"range\" class=\"anim-slider\"\n           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n           oninput=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.set_frame(parseInt(this.value));\"></input>\n    <div class=\"anim-buttons\">\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.slower()\"><i class=\"fa fa-minus\"></i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.first_frame()\"><i class=\"fa fa-fast-backward\">\n          </i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.previous_frame()\">\n          <i class=\"fa fa-step-backward\"></i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.reverse_animation()\">\n          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.pause_animation()\"><i class=\"fa fa-pause\">\n          </i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.play_animation()\"><i class=\"fa fa-play\"></i>\n          </button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.next_frame()\"><i class=\"fa fa-step-forward\">\n          </i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.last_frame()\"><i class=\"fa fa-fast-forward\">\n          </i></button>\n      <button onclick=\"animb1a36cca1fda41c7aef4a6f3b1a3ba14.faster()\"><i class=\"fa fa-plus\"></i></button>\n    </div>\n    <form action=\"#n\" name=\"_anim_loop_selectb1a36cca1fda41c7aef4a6f3b1a3ba14\" class=\"anim-state\">\n      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_b1a36cca1fda41c7aef4a6f3b1a3ba14\"\n             checked>\n      <label for=\"_anim_radio1_b1a36cca1fda41c7aef4a6f3b1a3ba14\">Once</label>\n      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_b1a36cca1fda41c7aef4a6f3b1a3ba14\"\n             >\n      <label for=\"_anim_radio2_b1a36cca1fda41c7aef4a6f3b1a3ba14\">Loop</label>\n      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_b1a36cca1fda41c7aef4a6f3b1a3ba14\"\n             >\n      <label for=\"_anim_radio3_b1a36cca1fda41c7aef4a6f3b1a3ba14\">Reflect</label>\n    </form>\n  </div>\n</div>\n\n\n<script language=\"javascript\">\n  /* Instantiate the Animation class. */\n  /* The IDs given should match those used in the template above. */\n  (function() {\n    var img_id = \"_anim_imgb1a36cca1fda41c7aef4a6f3b1a3ba14\";\n    var slider_id = \"_anim_sliderb1a36cca1fda41c7aef4a6f3b1a3ba14\";\n    var loop_select_id = \"_anim_loop_selectb1a36cca1fda41c7aef4a6f3b1a3ba14\";\n    var frames = new Array(5);\n    \n  frames[0] = 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Kl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\\\n/6+57B9//LF1zPv06SMOHjyocuI6Bw4cEA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BERJJiQRMRSYoFTUQkKRY0EZGkWNBERJJiQRMRSYoF\\\nTUQkKRY0EZGk/j9Kn6iMsaEQzAAAAABJRU5ErkJggg==\\\n\"\n\n\n    /* set a timeout to make sure all the above elements are created before\n       the object is initialized. */\n    setTimeout(function() {\n        animb1a36cca1fda41c7aef4a6f3b1a3ba14 = new Animation(frames, img_id, slider_id, 500.0,\n                                 loop_select_id);\n    }, 0);\n  })()\n</script>\n"
     },
     "metadata": {},
     "execution_count": 56
    }
   ],
   "source": [
    "stop_epsilon = 10**-4\n",
    "theta = theta_0\n",
    "pi = pi_0\n",
    "is_continue = True\n",
    "count = 1\n",
    "while is_continue:\n",
    "    s_a_history = goal_maze_ret_s_a(pi)\n",
    "    new_theta = update_theta(theta, pi, s_a_history)\n",
    "    new_pi  = softmax_convert_into_pi_from_theta(new_theta)\n",
    "    print(np.sum(np.abs(new_pi-pi)))\n",
    "    print(\"求解迷宫需要的步数：\"+str(len(s_a_history)-1))\n",
    "    if np.sum(np.abs(new_pi-pi)) < stop_epsilon:\n",
    "        is_continue = False\n",
    "    else:\n",
    "        theta = new_theta\n",
    "        pi = new_pi\n",
    "np.set_printoptions(precision=3,suppress=True)\n",
    "print(pi)\n",
    "\n",
    "from matplotlib import animation \n",
    "from IPython.display import HTML\n",
    "\n",
    "def init():\n",
    "    line.set_data([],[])\n",
    "    return (line,)\n",
    "\n",
    "def animate(i):\n",
    "    state = s_a_history[i][0]\n",
    "    x = (state % 3) + 0.5\n",
    "    y = 2.5 - int(state/3)\n",
    "    line.set_data(x,y)\n",
    "    return (line,)\n",
    "\n",
    "anim = animation.FuncAnimation(fig,animate,init_func=init,frames=len(s_a_history),interval=500,repeat=False)\n",
    "HTML(anim.to_jshtml())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}